GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 19 Dec 2018, 08:05

TODAY:

MIT Sloan R1 Decisions - Join MIT Chat for Live Updates | Chat with UCLA Anderson Adcom @9am PT | Chat with Yale SOM R1 Admit 10am PT


Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • Happy Christmas 20% Sale! Math Revolution All-In-One Products!

     December 20, 2018

     December 20, 2018

     10:00 PM PST

     11:00 PM PST

    This is the most inexpensive and attractive price in the market. Get the course now!
  • Key Strategies to Master GMAT SC

     December 22, 2018

     December 22, 2018

     07:00 AM PST

     09:00 AM PST

    Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.

How many integers from 1 to 100 are not divisible by 2, 3 and 5?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Manager
Manager
User avatar
S
Joined: 11 Sep 2013
Posts: 149
Concentration: Finance, Finance
How many integers from 1 to 100 are not divisible by 2, 3 and 5?  [#permalink]

Show Tags

New post Updated on: 27 Oct 2014, 01:34
2
13
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

61% (02:25) correct 39% (02:33) wrong based on 186 sessions

HideShow timer Statistics

How many integers from 1 to 100 are not divisible by 2, 3 and 5?

A. 26
B. 29
C. 31
D. 32
E. 41

Originally posted by Raihanuddin on 26 Oct 2014, 11:03.
Last edited by Bunuel on 27 Oct 2014, 01:34, edited 5 times in total.
Renamed the topic and edited the question.
Most Helpful Community Reply
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1825
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: How many integers from 1 to 100 are not divisible by 2, 3 and 5?  [#permalink]

Show Tags

New post Updated on: 26 Oct 2014, 21:14
5
7
Raihanuddin wrote:
How may integers from 1 to 100 are not divisible by 2, 3 and 5?
a. 25
b. 29
c. 31
d. 36
e.41


Numbers divisible by 2 = 50

Numbers divisible by 3 = 33

Numbers divisible by 5 = 20

Numbers divisible by 6 (LCM of 2 & 3) = 16

Numbers divisible by 10 (LCM of 2 & 5) = 10

Numbers divisible by 15 (LCM of 3 & 5) = 6

Numbers divisible by 30 (LCM of 2, 3 & 5) = 3

Numbers divisible by 2, 3 & 5 combined = 50 + 33 + 20 - (16 + 10 + 6) + 3 = 103 - 32 + 3 = 106 - 32 = 74

Numbers not divisible by 2, 3 & 5 = 100 - 74 = 26

Answer = A

Is the OA correct OR have I made some mistake?
_________________

Kindly press "+1 Kudos" to appreciate :)


Originally posted by PareshGmat on 26 Oct 2014, 19:04.
Last edited by PareshGmat on 26 Oct 2014, 21:14, edited 1 time in total.
General Discussion
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1825
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: How many integers from 1 to 100 are not divisible by 2, 3 and 5?  [#permalink]

Show Tags

New post 26 Oct 2014, 19:14
Raihanuddin wrote:
How may integers from 1 to 100 are not divisible by 2, 3 and 5?
a. 25
b. 29
c. 31
d. 36
e.41


We can take inspiration from Venn diagram as shown below:

Attachment:
ven.png
ven.png [ 7.11 KiB | Viewed 85803 times ]

_________________

Kindly press "+1 Kudos" to appreciate :)

Manager
Manager
User avatar
S
Joined: 11 Sep 2013
Posts: 149
Concentration: Finance, Finance
Re: How many integers from 1 to 100 are not divisible by 2, 3 and 5?  [#permalink]

Show Tags

New post 26 Oct 2014, 20:05
Have you got the answer using venn diagram?
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8696
Location: Pune, India
Re: How many integers from 1 to 100 are not divisible by 2, 3 and 5?  [#permalink]

Show Tags

New post 26 Oct 2014, 20:27
3
1
Raihanuddin wrote:
Have you got the answer using venn diagram?


The venn diagram doesn't give you the answer directly. You do have to do the calculations shown above.

Numbers divisible by 2 = 50

Numbers divisible by 3 = 33

Numbers divisible by 5 = 20

Numbers divisible by 6 (LCM of 2 & 3) = 16

Numbers divisible by 10 (LCM of 2 & 5) = 10

Numbers divisible by 15 (LCM of 3 & 5) = 6

Numbers divisible by 30 (LCM of 2, 3 & 5) = 3

Total = n(A) + n(B) + n(C) - n(A and B) - n(B and C) - n(A and C) + n(A and B and C) = 50 + 33 + 20 - 16 - 10 - 6 + 3 = 74

Number not divisible by 2, 3 or 5 = 100 - 74 = 26

Answer (A)

You can plug in the same numbers in a venn diagram and solve though using the formula will be more efficient here.
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

Manager
Manager
User avatar
S
Joined: 11 Sep 2013
Posts: 149
Concentration: Finance, Finance
Re: How many integers from 1 to 100 are not divisible by 2, 3 and 5?  [#permalink]

Show Tags

New post 26 Oct 2014, 20:41
yes, Karishma is correct.
By using formula we can get the answer easily.

Total = A+B+C -(sum of 2 overlap groups)+(all the three)+Neither
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1825
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: How many integers from 1 to 100 are not divisible by 2, 3 and 5?  [#permalink]

Show Tags

New post 26 Oct 2014, 21:18
Raihanuddin wrote:
Have you got the answer using venn diagram?


Its an illustration as pointed out by Karishma.....

Karishma: Thanks for the correction; Kudos to you :)
_________________

Kindly press "+1 Kudos" to appreciate :)

Manager
Manager
avatar
Joined: 15 Aug 2013
Posts: 53
Re: How many integers from 1 to 100 are not divisible by 2, 3 and 5?  [#permalink]

Show Tags

New post 08 Oct 2016, 04:39
2
Hi,

We may also consider that - from 1 to 100 -> 1/2 of the numbers will be divided by 2 and 1/2 will not.
Similarly, from 1-100 -> 1/3 of the numbers will be divided by 3 and 2/3 will not.
And, from 1-100 -> 1/5 of the numbers will be divided by 5 and 4/5 will not.

Hence, No of number which are not divisible by 2,3 and 5 = 100(1/2)(2/3)(4/5) = 80/3 = 26.666. Ignoring the decimal since no of numbers cant be decimal leaves us with 26.
Board of Directors
User avatar
P
Joined: 17 Jul 2014
Posts: 2616
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
GMAT ToolKit User Premium Member Reviews Badge
Re: How many integers from 1 to 100 are not divisible by 2, 3 and 5?  [#permalink]

Show Tags

New post 20 Nov 2016, 09:55
Raihanuddin wrote:
How many integers from 1 to 100 are not divisible by 2, 3 and 5?

A. 26
B. 29
C. 31
D. 32
E. 41


from 1 to 100, 50 numbers are even, and 50 are odd. therefore, we can eliminate right away 50 numbers.
now...multiples of 5...let's see the multiples of 5 that are not odd...
5, 15, 25, 35, 45, 55, 65, 75, 85, 95 - 10 numbers - another 10 numbers eliminated
multiples of 3 that are not multiples of 5 and are not odd...
3, 9, 21, 27, 33, 39, 51, 57, 63, 69, 81, 87, 93, 99 - another 14 eliminated.
50 - 10 - 14 = 26
answer is A.
Intern
Intern
avatar
Joined: 08 Jun 2011
Posts: 18
Re: How many integers from 1 to 100 are not divisible by 2, 3 and 5?  [#permalink]

Show Tags

New post 08 Jul 2017, 08:33
2
1
Such questions are easier to crack if you understand one simple logic -

From 1 to 100 -> 1/n of the numbers will be divisible by n, and (1-1/n) will not - provided n is a prime no.
For example, if we consider, 3(prime) then from 1-100 :
1/3 of the numbers will be divided by 3 and (1-1/3 =2/3) will not be.
Similarly, 1/5 of the numbers will be divided by 5 and 4/5 will not be.

Now this question is a cakewalk -
No of number which are not divisible by 2,3 and 5 = 100*(1/2)*(2/3)*(4/5) = 80/3 = 26.666.
Since, we cant have decimal, ans should be 26.
VP
VP
avatar
P
Joined: 07 Dec 2014
Posts: 1130
How many integers from 1 to 100 are not divisible by 2, 3 and 5?  [#permalink]

Show Tags

New post 08 Jul 2017, 11:54
Raihanuddin wrote:
How many integers from 1 to 100 are not divisible by 2, 3 and 5?

A. 26
B. 29
C. 31
D. 32
E. 41


can someone help me with my logic here?
If the number of integers from 1 to 100 that ARE divisible by 2, 3 and 5=3, (30, 60 and 90),
then the number of integers NOT divisible by 2, 3 and 5=100-3=97
Intern
Intern
avatar
Joined: 08 Jun 2011
Posts: 18
Re: How many integers from 1 to 100 are not divisible by 2, 3 and 5?  [#permalink]

Show Tags

New post 09 Jul 2017, 01:16
gracie wrote:
Raihanuddin wrote:
How many integers from 1 to 100 are not divisible by 2, 3 and 5?

A. 26
B. 29
C. 31
D. 32
E. 41


can someone help me with my logic here?
If the number of integers from 1 to 100 that ARE divisible by 2, 3 and 5=3, (30, 60 and 90),
then the number of integers NOT divisible by 2, 3 and 5=100-3=97


Hi Gracie,
the questions really asks for all numbers that are either divisible by 2, 3 or 5.
This means, 2, 4, 6, 8, ....so on
3, 6, 9, 12, .....
5, 10, 15, 20, ....

Of course LCM (eg- 6, 15, 30, etc ) will be double counted so we must be careful while doing such questions!!
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 9207
Premium Member
Re: How many integers from 1 to 100 are not divisible by 2, 3 and 5?  [#permalink]

Show Tags

New post 12 Aug 2018, 11:58
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: How many integers from 1 to 100 are not divisible by 2, 3 and 5? &nbs [#permalink] 12 Aug 2018, 11:58
Display posts from previous: Sort by

How many integers from 1 to 100 are not divisible by 2, 3 and 5?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.